Management Accounting and Financial Reporting
Question: A company wants to set up a sinking fund for the repayment of a loan of $100m at the end of four years. It makes equal deposits at the end of each month into a fund that earns interest at 22% p.a compounded monthly. Determine the size of each deposit and construct a sinking fund schedule
Computation of the sinking fund:
Note: S = is for the amount
i = is for interest
n = is for the time or years to pay
1 = is constant
The business is obliged to pay the loan after its usage. The accumulation of the fund by making periodic deposits is called sinking fund with additional interests. After computing the amount that is needed for payment, the company should pay the loan with an equal amount of deposits worth $1,318,436.605 monthly within 4 years.
Sinking Fund Schedule
Period
Deposit
Interest
Increase
Amount
1
1,318,436.605
0
1,318,436.605
1,318,436.605
2
1,318,436.605
24127.38987
1,342,563.995
2,661,000.600
3
1,318,436.605
48696.31098
1,391,260.306
4,052,260.906
4
1,318,436.605
74156.37457
1,465,416.680
5,517,677.586
5
1,318,436.605
100973.4998
1,566,390.180
7,084,067.766
6
1,318,436.605
129638.4401
1,696,028.620
8,780,096.387
7
1,318,436.605
160675.7639
1,856,704.384
10,636,800.771
8
1,318,436.605
194653.4541
2,051,357.838
12,688,158.609
9
1,318,436.605
232193.3026
2,283,551.141
14,971,709.750
10
1,318,436.605
273982.2884
2,557,533.429
17,529,243.180
11
1,318,436.605
320785.1502
2,878,318.580
20,407,561.759
12
1,318,436.605
373458.3802
3,251,776.960
23,659,338.719
13
1,318,436.605
432965.8986
3,684,742.858
27,344,081.577
14
1,318,436.605
500396.6929
4,185,139.551
31,529,221.128
15
1,318,436.605
576984.7466
4,762,124.298
36,291,345.426
16
1,318,436.605
664131.6213
5,426,255.919
41,717,601.345
17
1,318,436.605
763432.1046
6,189,688.024
47,907,289.369
18
1,318,436.605
876703.3955
7,066,391.419
54,973,680.788
19
1,318,436.605
1006018.358
8,072,409.778
63,046,090.566
20
1,318,436.605
1153743.457
9,226,153.235
72,272,243.801
21
1,318,436.605
1322582.062
10,548,735.296
82,820,979.097
22
1,318,436.605
1515623.917
12,064,359.214
94,885,338.311
23
1,318,436.605
1736401.691
13,800,760.905
108,686,099.216
24
1,318,436.605
1988955.616
15,789,716.521
124,475,815.737
25
1,318,436.605
2277907.428
18,067,623.949
142,543,439.685
26
1,318,436.605
2608544.946
20,676,168.895
163,219,608.580
27
1,318,436.605
2986918.837
23,663,087.732
186,882,696.312
28
1,318,436.605
3419953.343
27,083,041.074
213,965,737.387
29
1,318,436.605
3915572.994
30,998,614.069
244,964,351.456
30
1,318,436.605
4482847.632
35,481,461.700
280,445,813.156
31
1,318,436.605
5132158.381
40,613,620.081
321,059,433.237
32
1,318,436.605
5875387.628
46,489,007.709
367,548,440.946
33
1,318,436.605
6726136.469
53,215,144.179
420,763,585.125
34
1,318,436.605
7699973.608
60,915,117.786
481,678,702.911
35
1,318,436.605
8814720.263
69,729,838.050
551,408,540.961
36
1,318,436.605
10090776.3
79,820,614.349
631,229,155.310
37
1,318,436.605
11551493.54
91,372,107.891
722,601,263.201
38
1,318,436.605
13223603.12
104,595,711.008
827,196,974.209
39
1,318,436.605
15137704.63
119,733,415.636
946,930,389.845
40
1,318,436.605
17328826.13
137,062,241.770
1,083,992,631.615
41
1,318,436.605
19837065.16
156,899,306.929
1,240,891,938.544
42
1,318,436.605
22708322.48
179,607,629.404
1,420,499,567.948
43
1,318,436.605
25995142.09
205,602,771.498
1,626,102,339.446
44
1,318,436.605
29757672.81
235,360,444.309
1,861,462,783.755
45
1,318,436.605
34064768.94
269,425,213.252
2,130,887,997.007
46
1,318,436.605
38995250.35
308,420,463.597
2,439,308,460.605
47
1,318,436.605
44639344.83
353,059,808.426
2,792,368,269.031
48
1,318,436.605
51100339.32
404,160,147.750
3,196,528,416.781
After the construction of the sinking fund schedule, the company is bound to pay within 4 years monthly. Meaning, the company has a responsibility to pay the amount with the interest for 48 months. The total amount that the company needed to pay is worth $3,196,528,416.781 with the inclusion of the subjected 22% interest. Within the span of 4 years, it is advised that the company should not fail to pay this amount to avoid the accumulation of interest that will definitely invite the negative effect in the company’s financial statement and might diminish the trust from the banks, loaning institutions, and investors.
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